Wireless systems experience time-varying multi-path fading, whereby a transmitted signal propagates along multiple paths to a receiver causing fading of the received signal due to the constructive and destructive summing of the signals at the receiver. Antenna diversity (transmitting diversity, receiving diversity) is a technique for overcoming the effects of multi-path fading in wireless systems.
When multiple-antennas are available, the use of space-time codes provides diversity and coding gains that reduce the average error probability over fading channels. In ad-hoc network applications or in distributed large scale wireless networks, the nodes are often constrained in the complexity of their hardware and also in their size. This makes multiple-antenna systems impractical for certain networks.
Recently, several methods have been proposed for cooperation among relay nodes to provide spatial diversity gains without utilizing multiple transmit antennas. The decode-and-forward strategy is one such method that has been shown to provide various benefits in addition to being information theoretically optimal in certain scenarios. Common to all decode-and-forward strategies is the fact that the relays first decode the source message reliably and then relay it after re-encoding. Several methods have been proposed for forwarding the common message by the relays, from the simple repetition, to space-time coding to more idealistic approaches derived from an information theoretic framework established. In general, space-time coding is superior to repetition, since it provides diversity without a significant loss in spectral efficiency.
A major challenge in distributed cooperative transmissions is to find a way to coordinate the relay transmissions without requiring extra control information overhead, which would reduce part of the gain. The coding rule applied by each of the cooperating nodes should, therefore, be identical and independent from node to node. However, most of the distributed space-time codes in the literature do not focus on this issue. In the conventional schemes, each node emulates a specific array element of a multiple-antenna system; in practice, the implementation requires a centralized code allocation procedure. In addition, in large-scale distributed wireless networks, the set of cooperating nodes is unknown or random in most scenarios. For example, in networks with a single source-destination pair and multiple cooperating relays, the set of nodes that is responsible for retransmission is random due to the error-free decoding constraint. The randomness in the cooperating set may be due to fading, mobility, node failure, expired battery life, or the occurrence of a possible sleep state.
There is a need for codes that provide diversity gains in cooperative networks even when the number of cooperating nodes is unknown or random.
Other approaches that apply to a decentralized scenario have been proposed. In one instance, a protocol has been proposed where the relay nodes transmit with a randomly chosen delay. Hence, further diversity is obtained by intentionally creating a frequency selective channel. Note that this scheme may not provide diversity gains due to the possibility that each node may choose to use the same delay. In another instance, the nodes regenerate the signal at time instants that depend on the energy accumulated per symbol.
The decentralized policy produces diversity only if the delays can be resolved at the receiver, which in general requires a large bandwidth.
In some instances, coding rules have been proposed such that each cooperative node emulates a specific antenna of a multi-antenna system. Since the nodes need to know their specific antenna index, either inter-node communication or a central control unit is required for code assignment. In one instance, orthogonal space-time codes, which may become impractical for large number of nodes, are proposed. In another instance, a filtering approach has been proposed that does not require the knowledge of the number of cooperating nodes in order to achieve maximum diversity. In yet another instance, each node transmits the product of a space-time code matrix with a pre-assigned vector-code. As a result, this scheme does not require the knowledge of the number of cooperating nodes that are active, but it still requires a preliminary code allocation phase. In one way or another, most of these schemes become impractical in a self-organized network with a large and/or random number of nodes.